The invention relates generally to the field of evaluation of seismic events occurring in the subsurface. More particularly, the invention relates to method for evaluating physical properties of subsurface formations by determining spatial and temporal distribution of the Gutenberg-Richter parameter.
In earthquake seismology the Gutenberg-Richter law expresses the relationship between the magnitude and total number of earthquakes in any given region and time period of at least that magnitude. The law is generally expressed by the formula:log N=a−bM  (1)
wherein N represents the number of seismic events having a magnitude greater than or equal to a minimum magnitude, represented by M, and a and b are empirically determined constants. The relationship is surprisingly robust and does not vary significantly from region to region or over time when dealing with naturally occurring earthquakes (subsurface originating seismic events).
The constant b is typically equal to 1.0 in seismically active regions. This means that for every Richter magnitude 4.0 event there will be 10 Richter magnitude 3.0 events and 100 Richter magnitude 2.0 events. There is some variation of b values in the range 0.5 to 1.5 depending on the tectonic environment of the region. A notable exception is during earthquake swarms when the b value can become as high as 2.5, indicating an even larger proportion of small quakes to large ones. A b value significantly different from 1.0 may suggest a problem with the data set; e.g., it is incomplete or contains errors in calculating magnitude.
There is a tendency for the b value to decrease for smaller magnitude events. This effect is described as “roll-off” of the b value, a description due to the plot of the logarithmic version of the Gutenberg-Richter law becoming flatter at the low magnitude end of the plot. Data which perfectly follows Gutenberg Richter law plots on a straight line on a logarithmic scale. Formerly, “roll-off” in the b values was taken as an indicator of incompleteness of the data set. That is, it was assumed that many low-magnitude earthquakes were missed because fewer stations detect and record them. However, some modern models of earthquake dynamics have roll-off as a natural consequence of the model without the need for the feature to be inserted arbitrarily.
The a value generally believed to be of less scientific interest and simply indicates the total seismicity rate of the region. This is more easily observed when the Gutenberg Richter law is expressed in terms of the total number of events.
More recently, passive seismic monitoring has been applied to uses such as imaging subsurface formations without the need to use an active (controlled) seismic energy source, and in monitoring progress of subsurface formation treatments such as fracturing. The latter use includes the inducing seismic events as the formations are fractured by pumping fluid into a wellbore drilled through and hydraulically connected to certain subsurface formations. Such fracture treatment is used to increase the effective wellbore radius, so that formations containing economically useful materials such as hydrocarbons may be more effectively drained.
There is a need to determine spatial and temporal changes in the stresses induced in subsurface formations as a result of induced seismic events such as those caused by fracture treatment, so that predictions about the extent and geometry of the induced fractures may be made more accurately.